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人类认识客观世界,是从感性到理性、从整体到部分、从粗略到精细进行的。陈霖的拓扑知觉理论认为,人类视知觉加工的过程是从大范围的拓扑特征开始,按照不同几何变换的稳定性(从稳定到不稳定:拓扑变换—射影变换—欧氏变换)的次序进行的~([1])。脑科学研究表明,人类对数量的认知,具有估算和精算两个系统,是从估算到精算发展的。定性分析与定量分析相结合,既是估算与精算相结合的外在反映,也是从整体到部分、从粗略到精细、从拓扑到度量地认识客体的主要数学认知加工活动次序。定性分析和定量分析相结合的主要内涵是:个
Human beings understand the objective world, from sensibility to rationality, from the whole to the part, from rough to fine. According to Chen Lin’s theory of topological perception, the process of human visual perception processing starts from a large range of topological features and is performed in the order of the stability of different geometric transformations (from stable to unstable: topological transformation - projective transformation - Euclidean transformation) ~ ([1]). Brain science research shows that human cognition of the quantity, with the two systems of estimation and actuarial development, is from estimation to actuarial development. The combination of qualitative analysis and quantitative analysis is both an external reflection of the combination of estimation and actuarial calculation. It is also the order of major mathematical cognitive processing activities from the whole to the part, from coarseness to fineness, and from the topological to the metric understanding of the object. Qualitative analysis and quantitative analysis of the main connotation is: a